Question

If the polynomial 6x4−9x3−2x2+ax−bis exactly divisible by the polynomial 3x2−4, then find the values of a and b.

Answer 1

Answer:

a=12 b=8

Step-by-step explanation:

3x2 - 4 ) 6x4 - 9x3 - 2x2 + ax - b ( 2x2 + 3x + 2

6x4 - 8x2

- +

--------------

- 9x3 + 6x2

+ 9x3 - 12x

+ -

------------------

+ 6x2 + ax - 12x - b

+ 6x2 - 8

- +

-----------------

ax - 12x - b + 8 = 0

( a - 12 ) x + 8 - b = ( 0 ) x + 0

because it's given that the equation is exactly divisible by the quotient

a - 12 = 0 , 8 - b = 0

a = 12 , b = 8